The goal of this chapter is to perform an independent derivation of the hereditary processes up to 5PN order, to verify the results proposed in [1]}, and later explained in [2]} and [3]}, and the ones computed in [4]}. We want to shed new light in the computation of these processes, by constructing a new computational algorithm in Mathematica which starting from the effective action in the far zone introduced in Eq.(REF ), computes the Feynman rules, generate the diagrams and evaluates them using modern multi-loop techniques, and which can be generalized at arbitrary PN order.
From the multipole action (REF ) we can generate a wide variety of triple multipole diagrams following the power counting rules described in the previous chapter REF .
